Bosco

Of the 80 spaces in the XYZ Industries' parking lot, 5% of them are reserved for handicapped parking. Of the non-handicapped spaces, 16 are reserved for company VIPS. How many spaces that are NOT reserved for handicapped parking are available to non-VIP employees?     

80 – (80)(5%)    =     

80 – (80)(0.05)  =     

80 – 4                =  76 for non-handicapped     

76 – 16              =  60 for non-VIP     

_.     

Find all possible ways of numbering two 6-sided dice with positive integers (not necessarily distinct), so that when they are rolled, the 36 possible outcomes for the sum of the two rolls are the same as the 36 possible outcomes for the sum of two standard 6-sided dice.     

There's an infinite amount of integers to choose from, so     

you can re-number the first die any way you want to, just as     

long as you re-number the second die the same way as the     

first.  I don't like to use infinity as a number, but you never     

come to the last number, so I have to.     

Rolling one die twice is the same as rolling two dice once.     

_.     

Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 2x^2 + 12x - 7.     

                                             y  =  –2x² + 8x – 15 – 2x² + 12x – 7     

                                             y  =  –4x² + 20x – 22     

take 1^st derivitive                  y'  =  –8x + 20     

set 1^st deriv equal zero        –8x + 20  =  0     

                                                     –8x  =  –20     

                                                         x  =  2.5     <<—  this is the x-coordinate of the vertex     

The first derivitive is the slope of the curve at any point.  When the slope is zero, that     

means there's no slope, i.e., the curve is turning around and going the other direction.

plug 2.5 into equation            y  =  (–4)(2.5²) + (20)(2.5) – 22     

                                              y  =  –25 + 50 – 22     

                                              y  =  3                    <<—  this is the y-coordinate of the vertex     

so the vertex is located at     (2.5,  3)     

_.     

A person is looking from a car to the top of a building. The angle of elevation to the top of the building from the car is 32°. The building is 200 feet away. How tall is the building? Round to the nearest foot.     

     tangent equals opposite over adjacent     

     tan(32)  =  x / 200     

     0.62487  =  x / 200     

     x  =  200 • 0.62487     

     x  =  124.97     to the nearest foot is 125     

_.     

Ms. Rathman has 5 nickels, 3 dimes, and 2 quarter. In how many ways can she make change for 50¢?     

25  25     

25  10  10  5     

25  10  5  5  5     

25  5  5  5  5  5     

10  10  10  5  5  5  5           I count 5 ways.  If you find another, give me a call.     

_.     

Amanda and her group of friends spent a total of 35.50 on 7 hot dogs and 6 cheese burgers. Greg and his group of friends spent 30.50 at the same snack bar on 5 hot dogsand 6 cheese burgers. For your answer WRITE THE EQUATIONS and state how much hot dogs cost and cheese burgers cost.     

                    7D + 6B  =  35.50     

                    5D + 6B  =  30.50     

                    2D           =  5.00     

                               D  =  2.50     

                    (7)(2.50) + 6B  =  35.50     

                         17.50 + 6B  =  35.50     

                                      6B  =  18.00     

                                        B  =  3.00     

_.